Correlation and Regression 2

Front

What is correlation in statistics?

Back

Correlation is a statistical measure that describes the extent to which two variables change together. A positive correlation means that as one variable increases, the other also increases, while a negative correlation means that as one variable increases, the other decreases.

Front

What does the correlation coefficient (r) indicate?

Back

The correlation coefficient (r) quantifies the strength and direction of a linear relationship between two variables, ranging from -1 to 1. An r value close to 1 indicates a strong positive correlation, while an r value close to -1 indicates a strong negative correlation.

Front

What is a residual plot?

Back

A residual plot is a graph that shows the residuals on the vertical axis and the independent variable on the horizontal axis. It helps to assess the fit of a regression model by showing if the residuals are randomly dispersed.

Front

What does it mean if a residual plot shows a random pattern?

Back

If a residual plot shows a random pattern, it indicates that a linear regression model is appropriate for the data, as it suggests that the model's assumptions are met.

Front

What is the effect of adding a constant to all values of the y-variable on the correlation coefficient?

Back

Adding a constant to all values of the y-variable does not affect the correlation coefficient; it remains the same.

Front

What happens to the correlation coefficient if you interchange the x and y variables?

Back

Interchanging the x and y variables does not change the value of the correlation coefficient; it remains the same.

Front

What is a positive association in a scatter plot?

Back

A positive association in a scatter plot indicates that as the x-values increase, the y-values also tend to increase, resulting in an upward trend.

Front

What is a negative association in a scatter plot?

Back

A negative association in a scatter plot indicates that as the x-values increase, the y-values tend to decrease, resulting in a downward trend.

Front

What does a correlation coefficient of r = 0 indicate?

Back

A correlation coefficient of r = 0 indicates no linear relationship between the two variables.

Front

What is the purpose of linear regression?

Back

The purpose of linear regression is to model the relationship between a dependent variable and one or more independent variables, allowing for predictions and analysis of trends.